Respuesta :
Answer: The correct option is
(D) [tex]\dfrac{4}{77}.[/tex]
Step-by-step explanation: Given that a bag of coins contains 6 quarters, 4 dimes, 5 nickels, and 7 pennies.
We are given to find the probability of drawing a dime then a quarter, without replacement.
Total number of coins = 6+4+5+7 = 22.
Let A represents the event of drawing a dime and B represents the event of drawing a quarter without replacement after drawing a dime.
Then, the probabilities of A and B are
[tex]P(A)=\dfrac{\textup{number of dimes}}{\textup{total number of coins}}=\dfrac{4}{22}=\dfrac{2}{11}[/tex]
and
[tex]P(B)=\dfrac{\textup{total number of quarters}}{\textup{total number of coins left after drawing a dime}}=\dfrac{6}{21}=\dfrac{2}{7}.[/tex]
Therefore, the probability of drawing a dime then a quarter, without replacement is given by
[tex]P(A\cap B)\\\\=P(A)\times P(B)~~~~~~~~~~~~~~~~~~~[\textup{since A and B are independent events}]\\\\\\=\dfrac{2}{11}\times\dfrac{2}{7}\\\\\\=\dfrac{4}{77}.[/tex]
Thus, the required probability is [tex]\dfrac{4}{77}.[/tex]
Option (D) is CORRECT.
